TY - JOUR
T1 - Stability and Error Analysis of SAV Semi-Discrete Scheme for Cahn-Hilliard-Navier-Stokes Model
AU - Gao , Haijun
AU - Li , Xi
AU - Feng , Minfu
JO - Numerical Mathematics: Theory, Methods and Applications
VL - 1
SP - 66
EP - 102
PY - 2025
DA - 2025/04
SN - 18
DO - http://doi.org/10.4208/nmtma.OA-2024-0050
UR - https://global-sci.org/intro/article_detail/nmtma/23942.html
KW - Cahn-Hilliard-Navier-Stokes, fully decoupled, scalar auxiliary variable (SAV), energy stability, error estimates.
AB - <p style="text-align: justify;">We construct first- and second-order time semi-discretization numerical
schemes for the Cahn-Hilliard-Navier-Stokes model. This discretization scheme is
based on the energy form of the scalar auxiliary variable approach for the coupling
terms of model and pressure correction in the Navier-Stokes equations, which are
fully decoupled. Then, we apply the fully explicit forms and the two scalar auxiliary
variables to obtain stable unconditional energy over time. At the same time, we
present the error analysis for the first-order scheme and the convergence rate for all
relevant variables in different norms. Finally, numerical examples are presented to
validate the theoretical analysis.</p>